System and method for characterizing a printing device

ABSTRACT

A method is used for constructing a look up table for characterizing a printing device, and a system therefore, wherein the look up table is an inverse look up table for obtaining for the printing device colorant values in a colorant space as a function of given color values in a color space. The method includes: (a) selecting an axis in the color space; (b) selecting a path in the color space; (c) determining a particular point on the path having a predetermined colorant value; (d) projecting the particular point on the axis, thus obtaining a projected point; and (e) adding the projected point to the look up table as a sampling point.

FIELD OF THE INVENTION

The present invention relates to the field of image rendering by meansof printing devices, particularly multicolor output devices; theinvention especially concerns characterization of these devices.

BACKGROUND OF THE INVENTION AND DEFINITION OF TERMS

Today, more and more printing systems are developed for the reproductionof color images. Several printing technologies are used such asconventional photography, electrophotography, thermal transfer, dyesublimation and ink jet systems to name a few.

All these systems can be described as multidimensional color printerswith n colorants, such as the CMYK (cyan, magenta, yellow and black)inks of an ink jet system. In this document it is assumed that thecolorant values range from 0% (no colorant laid down on the receivingsubstrate such as paper) to 100% (maximum amount of colorant laid downon the receiving substrate).

With colorant space is meant an n-dimensional space with n the number ofindependent variables with which the printer can be addressed. In thecase of an offset printing press the dimension of the space correspondsto the number of inks of the printer. When CMYK inks are used, thedimension of the colorant space is normally four.

The colorant gamut is defined by the possible combinations of thecolorant values, normally ranging from 0% to 100%. If there are nocolorant limitations, the colorant gamut is a n-dimensional cube.

With color space is meant a space that represents a number of quantitiesof an object that characterize its color. In most practical situations,colors will be represented in a 3-dimensional space such as the CIE XYZspace. However, also other characteristics can be used such asmulti-spectral values based on filters that are SUBSTITUTE SHEET (RULE26) not necessarily based on a linear transformation of the colormatching functions to represent color.

A printer model is a mathematical relation that expresses color valuesas a function of colorants for a given printer. The variables for thecolorants are denoted as c₁, c₂, . . . , c_(n), with n the dimension ofthe colorant space. An n-ink process is completely characterized by itscolorant gamut with a number of colorant limitations and the printermodel. Because of this close relationship between an n-ink process andthe printer model, the operations typical for a printer model are alsodefined for the n-ink process.

The printer model is often based on a printer target. Such a targetconsists of a number of uniform color patches, defined in the colorantspace of the printing device. The printer target is printed andmeasured, and based on the values of the patches in colorant space andthe measured values, the printer model is made. A printer target isnormally based on a number of sampling points along the differentcolorant axes. Based on the sampling points a regular grid can beconstructed in colorant space of which a number of grid points arecontained by the printer target. Hence a target can be said to becomplete or incomplete (see EP-A-1 146 726 for complete and incompleteprinter targets).

Creating the printer model is also called characterizing the printer;this is an important step in the consistent reproduction of images.Before a printer is characterized, it is first calibrated, i.e. put in astandard state. When the printer model is created, it can be inverted inorder to obtain a so-called characterization transformation (or inverseprinter model). The characterization transformation transforms givencolors from color space (typically CIELAB) to the colorant space of theprinting device, whereas the printer model transforms given colorantvalues in the colorant space of the printer to color values in colorspace.

The calculation of the correct amounts of colorant for the rendering ofcolor images on a printer is also called the color separation problem.Most of the color separation strategies known in the art comprise thefollowing steps.

In a first step, the relation between the amounts of colorants and theresulting colors on a printer is characterized. This is done by firstprinting a set of colorant combinations that spans the dynamic range ofthe printer and measuring the resulting colors. An example of such a setis the ANSI IT8.7/3 reference target.

In a second step this relation is mathematically modeled, to obtain theprinter model. The printer model usually consists of some form of ananalytical expression that predicts color for a given combination ofcolorant amounts.

In a third step the printer model is inverted. This is necessary sincethe color separation problem is involved with finding a set of colorantsthat renders a given color and not vice versa.

Different types of printer models can be used, ranging from analyticalmodels simulating the printing process, over polynomials approximatingthe global behavior of the printer, to localized approximations of theprinter in the colorant domain.

An important advantage of localized models is that a simple mathematicalexpression is used to represent the printer behavior. For such anapproach, in most cases the colorant cube is divided into cells that areall modeled separately. A disadvantage is that, at boundaries ofneighboring cells, the model is not continuous for the first derivativeand hence sometimes slope discontinuities in the modeling can be seen.

In characterizing printing devices, in most cases multi-dimensional LookUp Tables (LUT's) are used. A typical example of such a characterizationsystem is represented by the ICC profile format (ICC stands forInternational Color Consortium). For printers, both the forward and theinverse relation is needed. The forward relation, embodied in theforward LUT, predicts the color values in function of given colorantvalues, i.e. it represents the printer model. The inverse relation,embodied in the inverse LUT, gives the colorant values required toobtain given color values, i.e. it represents the characterizationtransformation of the printer.

A LUT is often characterized by a number of sampling points (or samplingvalues) per axis. Based on these sampling points, usually a regular gridis constructed. However, it is also possible to construct LUT's withnon-regular grids. Also in this case the LUT's can be characterized bysampling points per axis but not all combinations of the sampling pointsof the different axes result in grid points. We refer to patentapplication EP-A-1 146 726 for more information on grids, printermodels, complete and incomplete printer targets, and related terms, andto patent application EP-A-1 083 739 for more information oncalibration, characterization, and other relevant terms.

In known systems, the sampling points of a LUT are chosen atpredetermined values, e.g., for sampling points along a colorant axis c,at colorant values c=0%, 25%, 50%, 75% and 100%.

Several printers have, for one or more of the colorants, multi-densityinks, i.e. two or more inks that have a different density and a similarhue, e.g. light cyan and heavy cyan. By means of multi-density inks, theapparent visual resolution of the printed images can be increased.Multi-density inks can be used in several ways; however, if thecalibration is based on 1-ink processes, the relation between themulti-density inks is fixed. If there is a light and heavy ink for cyanfor example, a relation is given that converts a global cyan value to alight and a heavy cyan value. Hence the printer is still considered as aCMYK device, but internally the global ink values can be converted tomulti-density ink values. The relation between a global ink value for aparticular colorant and the multi-density ink values is given by an inksplitting table, also called ink mixing table.

There is still a need for an improved method for characterizing aprinting device.

SUMMARY OF THE INVENTION

The present invention is a method for characterizing a printing deviceas claimed in independent claim 1, and a system therefore as claimed inclaim 11. Preferred embodiments of the invention are set out in thedependent claims. Preferably, a method in accordance with the inventionis implemented by a computer program as claimed in claim 13.

The present invention concerns the selection of sampling points for aninverse look up table for the characterization of a printing device. Ina preferred embodiment of the invention, a particular point on a path incolor space is determined that has a predetermined colorant value, and aprojection of this particular point on an axis in color space is takenas a sampling point of the inverse look up table.

The axis in color space may be L* in CIELAB space.

In one embodiment of the invention, the path in color space coincideswith the axis, i.e. the particular point is directly determined on theaxis in color space.

In a preferred embodiment, the particular point is determined by meansof color separation values of a plurality of points on the path in colorspace.

An advantage of the invention is that it allows a smooth representationof color changes in the reproduced images.

Further advantages and embodiments of the present invention will becomeapparent from the following description and drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is described with reference to the following drawingswithout the intention to limit the invention thereto, and in which:

FIG. 1 shows an embodiment of the invention;

FIG. 2 shows color separation curves for the color values of the path ofFIG. 1;

FIG. 3 shows a color separation curve for the L* axis in CIELAB space;

FIG. 4 shows an ink mixing table;

FIG. 5 represents a graph of CIE lightness L* for the ink mixing tableof FIG. 4.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 shows a path 55 in a color space 50. In the embodiment of FIG. 1,the color space is CIELAB. Points 56-60 are located on path 55 atrespectively coordinates p=0%, 25%, 50%, 75% and 100%. In a particularembodiment, path 55 represents a specific Pantone™ color; in that case,point 57 is the location in CIELAB of the point that corresponds to 25%of this specific Pantone™ color.

FIG. 2 represents color separation curves 75-78 for path 55. In theshown embodiment, the colorant space is CMYK, and curves 75-78 are thecolor separation curves in respectively C, M, Y and K. These colorseparation curves may be determined as follows. For example for point57, with p=25%, the coordinates in color space 55 are taken and thecorresponding colorant values are computed via the inverse printermodel. The thus obtained colorant values c_(C), c_(M), c_(Y), c_(K), forrespectively C, M, Y and K, are put in ordinate for the abscissa valuep=25%. This is repeated for a number of points along path 55.

In order to select a sampling point for the inverse look up table forcharacterizing the printing device, color separation values, asrepresented by the curves in FIG. 2, may be used as follows. In a firstembodiment, a predetermined colorant value is taken, e.g. colorant value71 in FIG. 2, which is c_(C)=40%. The point on path 55 that has thispredetermined colorant value 71 is determined, i.e. point 63, see FIG.2, by means of color separation curve 75. As shown in FIG. 3, point 63is then projected on an axis in color space 50, e.g. axis 51 whichrepresents L*, thus obtaining projected point 83. The L*-value of point83 is taken as a sampling point along the L* axis. In general, such apoint 63 having a predetermined colorant value 71 may also be determinedwithout using the color separation curves 75-78; this will beillustrated further below. In a second embodiment, the color separationvalues (as shown in FIG. 2) are analyzed for at least one colorant.Based on the analysis, a point on path 55 is determined, such as point64 (see FIG. 2) that corresponds to a local extremum 74 (in this case alocal maximum) of separation curve 78 for K. As shown in FIG. 3, thispoint 64 is again projected on an axis in color space, resulting inprojected point 84, which also yields a sampling point along the L*axis.

An advantage of the invention is that points where the printing devicehas a peculiar behavior can be selected as sampling points, whichresults in better quality of the reproduced images, such as a smoothrepresentation of color changes. This selection of sampling points isopposed to the prior art, where predetermined sampling points are used.

The effects of the invention can easily be shown for the reproduction ofneutral colors, i.e. white, grays and blacks, and this especially forlow GCR (Gray Component Replacement) values. Low GCR means that the grayvalues are made with almost a minimal amount of black, i.e., for a CMYKprinting device, mainly with CMY. If a minimal amount of black is usedfor reproducing gray values, the gray values are reproduced in a veryunstable way. This means that a small change of the colorant values hasa maximal effect on the required color. If however, a maximal amount ofblack is used (high GCR), the grays are reproduced in a very stable way.This effect can be easily seen as changes in the CMY values often inducea small color shift of the neutrals and this shift changes in most casessmoothly from a dark gray to a light gray. Errors in the neutral colorsare easily noticed as the human visual system is very sensitive forneutrals. Moreover, the neutral colors are difficult to reproduce.Therefore, sampling points along a path corresponding to a neutralcolor, e.g. sampling points along the L* axis in CIELAB space, are veryimportant. In CIELAB space, colors for which a* and b* are zero areconsidered to be neutral. For neutrals, the lightness component L*varies from 0 to 100, wherein 0 corresponds to black and 100 to purewhite. In CIELAB, it is thus important to choose a proper sampling alongthe lightness axis.

This importance is emphasized by the embodiment of FIG. 1, whereinpoints 63 and 64 are projected onto the L* axis. Moreover, in a specificembodiment of the invention, the path 55 in color space 50 on which aparticular point 63, 64 is determined, and the axis 51 on which theparticular point 63, 64 is projected, coincide with each other. In otherwords, the particular point 63, 64 is then determined directly onto theaxis in color space. In CIELAB space, this axis is preferably the L*axis.

If the sampling points are directly determined onto the L* axis, thisallows accurate rendering of a color vignette (showing gradual colorchanges) for neutrals. In case the sampling points are determined by theintermediate of a path 55 representing a specific Pantone™ color, asdiscussed above with reference to FIG. 1, this allows accurate renderingof a color vignette of this specific Pantone™ color.

FIG. 3 shows a color separation curve 79 for the L* axis in CIELABspace. Curve 79 gives the relation between a single colorant value, c,in ordinate, and L* in abscissa. If the colorant space is CMYK, then cis either c_(C), c_(M), c_(Y) or c_(K). As mentioned before, it isadvantageous to select points where the printing device has a peculiarbehavior as sampling points. For the separation curve 79 of neutrals,shown in FIG. 3, such points are points 91-95. The L* valuescorresponding to these points, such as L*=L₁ for point 95, are thentaken as sampling values along the L* axis. As mentioned already above,the sampling points may be determined in two different ways. In thefirst embodiment mentioned above, one starts from a predeterminedcolorant value, while in the second embodiment, a color separation curveis analyzed and the sampling point results from the analysis. Bothembodiments are discussed now with respect to FIG. 3.

In the first embodiment, a predetermined colorant value 72, 73 is taken,such as c=40% or c=70% in FIG. 3. Such a predetermined colorant value72, 73 may correspond to a printer model boundary point 94, 95 of theprinting device, i.e. a point at a boundary of a cell of a localizedprinter model, as discussed already above. A predetermined colorantvalue 72, 73 may also correspond to a point that is called an inkchanging point in this document. Ink changing points occur in case of aprinting device with multi-density inks, at values for which amulti-density ink changes non-smoothly. Ink changing points arediscussed further below, with reference to FIG. 4. In FIG. 4, c=40% andc=70% are ink changing points. Returning to FIG. 3, the L* values ofpoints 94 and 95, i.e. L*=L₁ and L*=L₂, are taken as sampling valuesalong the L* axis. An advantage of taking ink changing points andprinter model boundary points as sampling points is that the printerbehavior at such points is often non-smooth. For printer model boundarypoints, it was already discussed above that at such points sometimesslope discontinuities in the modeling can be seen. The non-smoothbehavior at ink changing points is now discussed with reference to FIGS.4 and 5.

As mentioned already above, if a printing device has multi-density inksfor at least one of its colorants, and the calibration is based on 1-inkprocesses, customarily an ink splitting table (or ink mixing table) isused. Such an ink splitting table gives the relation between a globalink value for the colorant for which multi-density inks are used and themulti-density ink values.

FIG. 4 shows an ink mixing table 40 for a light and a heavymulti-density ink of a particular colorant (e.g. cyan). FIG. 4 gives theamount of light ink, curve 21, and the amount of heavy ink, curve 22, asa function of the global colorant value c for the particular colorant,which is indicated along axis 10. In the embodiment of FIG. 4, theamount of light ink 21 reaches a maximum at a global colorant value ofc=40% and then decreases to zero at c=70%. The amount of heavy ink 22 onthe other hand increases from zero, at c=40%, up to a maximum reached atc=100%. The amounts of light and heavy ink are given by the ordinatevalues of curves 21 and 22, i.e. by the values along axis 20. In FIG. 4,the maximum amount for the light ink is 52% and that for the heavy ink73%. As is the case in the embodiment depicted in FIG. 4, the maximumamounts do not have to be 100% but can be lower, in order to reproducecolors with less ink.

The behavior of the ink mixing table of FIG. 4 is not smooth at c=40%and c=70%. This behavior in most cases induces a non-smooth change inthe color values. In FIG. 5 one of the color values, CIE lightness L*,is represented for the mixing of the inks represented in FIG. 5. FIG. 5indeed shows a non-smooth change of lightness L* for c=40% and c=70%, asindicated by the solid curve 23 (remark: in FIG. 5, point c=0% of curve23 has a high value of L*, e.g. L*=100 if L* is determined with respectto the so-called ‘white of the paper’, while point c=100% of curve 23has a low value of L*, e.g. L*=40). If the forward look up table of theprinting device contains the sampling points 16 and 17 at c=40% andc=70%, the coordinates of the points 28 are known and hence the printermodel can predict this non-smooth behavior. If however the forward lookup table does not contain these sampling points 16, 17, but for exampleonly the sampling points 11-15 at respectively c=0%, 25%, 50%, 75% and100%, only the coordinates of the points 27 are known. There is thus noinformation available of the color behavior at c=40% and 70%, and hencethe model will not be able to predict the non-smooth effects at c=40%and 70%. The L* values predicted by a printer model based on samplingpoints 11-15 is shown in FIG. 5 by the dotted curve 24. The errors madeat c=40% and 70% are quite serious; they are indicated by the linesegments 31 and 32, which are the differences between the ordinatevalues of the solid curve 23 and the dotted curve 24.

As is clear from the explanation above, to model the printer properly incase of multi-density inks and the use of ink mixing tables, it isadvantageous to include the values for which a multi-density ink changesnon-smoothly. The points that correspond to these values are called inkchanging points in this document. Typical ink changing points correspondto values at which an additional ink starts (in FIG. 4: c=40% for curve22 of the heavy ink), at which an ink reaches a maximum (c=40% for curve21 of the light ink), becomes constant, or zero (c=70% for curve 21 ofthe light ink). Mathematically speaking, at an ink changing point thederivative of the ink mixing table is not continuous and hence the inkmixing table has a non-smooth behavior at the ink changing point.

The above discussion with respect to FIG. 5 is related to a forward LUT.However, also for the inverse LUT it is advantageous to include one ormore, and preferably all ink changing points as sampling points. Usingsuch an inverse LUT results in smaller errors and better colorreproduction.

In FIG. 3, points 94 and 95 may be determined by starting from apredetermined colorant value, namely colorant value 73 respectively 72,and by using color separation curve 79. However, points 94 and 95 mayalso be determined without using a separation curve, e.g. by means of aniterative process. Suppose that the colorant space is CMYK and the colorspace is CIELAB. A predetermined colorant value 72 is given, e.g.c_(C)=40% (see also FIG. 3). Moreover, a GCR value is given. Now,iteratively, by using the printer model, the point on the L* axis isdetermined that has these values. By means of an iterative searchstrategy, the colorant values CM for M and cy for Y are varied untilpoint 95 is determined, i.e. the result of the iterative process will beL*=L₁ and a*=b*=0.

In the second embodiment discussed already above, a color separationcurve is analyzed, or, which amounts to the same thing, color separationvalues for a plurality of points on a path in color space are analyzed,and a sampling point results from the analysis. This embodiment isdiscussed now with respect to FIG. 3.

FIG. 3 shows that the separation curve 79 of neutrals has a peculiarbehavior at points 91-95. These points 91-95 can be found by analyzingcurve 79. Points 91-95 are slope discontinuities, i.e. points where theslope of curve 79, or in other words the first derivative of the curve,is not continuous. Point 92 is also a local extremum, in this case alocal minimum. As mentioned already above, a slope discontinuity may bean ink changing point or a printer model boundary point. A slopediscontinuity may also originate from other sources, such as: a non-wellbehaved CMYK process; a sudden change in the GCR behavior in case of aCMYK printer; a sudden change resulting from an imperfect printer model.Points 91-93 on curve 79 may be caused by a singularity in the CMYKprocess, where two different curves in CMYK space are mapped onto thesame point in CIELAB space. A typical example of an imperfect printermodel occurs in the case of a cyan, green, yellow process. Here, thegreen can be made by combining cyan with yellow, so that there are insome cases multiple solutions to obtain a given color.

Using local extrema, slope discontinuities, or both to determinesampling points is important in order to obtain accurate colorrendering, as is clear from the discussion with respect to FIG. 5 above.

Finding a local extremum by analyzing a color separation curve isstraightforward and will not be discussed. Finding a slope discontinuitycan be done as follows. The color separation curve is calculated for twohundred fifty-six equidistant abscissa values x_(i) (i=0 to 255 with astep of 1, denoted as i=0(1)255, i.e. i=0, 1, 2, . . . 255), wherein thefirst value x₀ of these equidistant values corresponds to the firstpoint of the color separation curve, and the last value x₂₅₅ correspondsto the last point of the color separation curve (for example, in FIG. 3,if the first point of curve 79 would have a value L*=30, and the lastpoint has, as indicated, a value L*=100, then x₀=30, x₂₅₅=100, and thedistance between x_(i) and x_(i+1) is 0.27=(100−30)/(256−1)). For anabscissa value x_(i), the calculated value is the ordinate value y_(i),so that the curve is now given by two hundred fifty-six points (x_(i),y_(i)). The vector between two consecutive points (x_(i−1), y_(i−1)) and(x_(i), y_(i)) is denoted as [(x_(i−1), y_(i−1))->(x_(i), y_(i))]. Theangle theta_(i) is calculated between two consecutive vectors [(x_(i−1),y_(i−1))->(x_(i), y_(i))] and [(x_(i), y_(i))->(x_(i+1), y_(i+1))] fori=1(1)254. Theta_(i) is defined as the angle between the extension ofvector [(x_(i−1), y_(i−1))->(x_(i), y_(i))] (which is the line segmentstarting in (x_(i), y_(i)) and having the direction of [(x_(i−1),Y_(i−1))->(x_(i), y_(i))]) and vector [(x_(i), y_(i))->(x_(i+1),y_(i+1))]; theta_(i) is positive in counter-clockwise direction and isin the range from −180° to 180°. A slope discontinuity is now defined asa point (x_(i), y_(i)) where the absolute value of theta_(i) is largerthan 10°.

In case of a plurality of color separation curves, e.g. four colorseparation curves for respectively C, M, Y and K, it is preferred thateach of these curves is analyzed. The sampling points resulting fromeach analysis are then put together to form a set of sampling points(along a path or axis, such as the L* axis). Moreover, additionalsampling points may be added to this set, e.g. by each time halving thelargest interval between two succeeding sampling points. In this way, apredetermined number of sampling points may be obtained.

In FIG. 1, points 63 and 64 are projected onto the L* axis, axis 51.Points 63 and 64 may also be projected on another axis in color space50, e.g. on the a* axis, axis 52, or on the b* axis, axis 53, or onboth. In this way, sampling points along these other axes (e.g. alongthe a* and the b* axis) may be obtained.

An example of points on a curve 55 in color space 50 is the use of aspecific Pantone™ color. Another example is related to the use ofabsolute and relative calorimetric values. Suppose that the color spaceis CIELAB and that the receiving substrate is not white but yellowpaper, with L*=90, a*=0 and b*=5. If the neutral colors are nowdetermined relatively with respect to this yellow paper, their absolutecolorimetic values do not coincide with the L* axis but are located on acurve in CIELAB space.

The present invention is concerned with selecting one or more samplingpoints for an inverse look up table for characterizing a printingdevice. A sampling point may be an ink changing point or another point,as discussed above. In one embodiment of the present invention, a path55 and an axis 51 in a color space 50 are selected. The path and theaxis may coincide; moreover, they may coincide with the L* axis inCIELAB space.

The invention was discussed especially with respect to CMYK ink jetprinters, but the present invention is not limited to the embodimentsdiscussed above. The invention is also applicable to printing devicesusing other printing technologies, such as electrophotography, thermaltransfer, dye sublimation. Other colors than CMYK may be applied; theprinter may have more, or less, than four colorants.

Having described in detail preferred embodiments of the currentinvention, it will now be apparent to those skilled in the art thatnumerous modifications can be made therein without departing from thescope of the invention as defined in the appending claims.

LIST OF REFERENCE SIGNS

-   10: colorant axis-   11-17: sampling point-   16: ink changing point-   17: ink changing point-   20: ink amount-   21-24: curve-   27: point-   28: point-   31: error-   32: error-   40: ink mixing table-   50: color space-   51-53: axis-   55: path-   56-60: point on path-   63,64: point-   71-73 colorant value-   74: local extremum-   75-79: color separation curve-   80: ink changing point-   83,84: projected point-   91-95: slope discontinuity-   92: local extremum-   94,95: ink changing point

1. A method for constructing a look up table for characterizing aprinting device, wherein said look up table is an inverse look up tablefor obtaining for said printing device colorant values in a colorantspace as a function of given color values in a color space, the methodcomprising the steps of: selecting an axis in said color space;selecting a path in said color space; determining a particular point onsaid path having a predetermined colorant value; projecting saidparticular point on said axis, thus obtaining a projected point; andadding said projected point to said look up table as a sampling point.2. The method according to claim 1 further comprising the steps of:determining color separation values in said colorant space for aplurality of points on said path; and using said color separation valuesin determining said particular point on said path.
 3. The methodaccording to claim 1 wherein said predetermined colorant value isselected from a group consisting of a colorant value of an ink changingpoint of said printing device and a colorant value of a printer modelboundary point of said printing device.
 4. The method according to claim1 wherein said path corresponds to a neutral color in said color space.5. The method according to claim 1 wherein said color space is CIELABand said axis is CIE L*.
 6. The method according to claim 1 wherein saidpath coincides with said axis.
 7. The method according to claim 1further comprising the steps of: projecting said particular point on asecond axis, thus obtaining a second projected point; and adding saidsecond projected point to said look up table as a another samplingpoint.
 8. The method according to claim 6 wherein a second axis isselected from a group consisting of CIE a* and CIE b*.
 9. The methodaccording to claim 3 further comprising the step of: adding all inkchanging points of said printing device to said look up table assampling points.
 10. The method according to claim 1 wherein saidprinting device is an ink jet printer.
 11. A system for constructing alook up table for characterizing a printing device, wherein said look uptable is an inverse look up table for obtaining for said printing devicecolorant values in a colorant space as a function of given color valuesin a color space, the system comprising: means for selecting an axis insaid color space; means for selecting a path in said color space; meansfor determining a particular point on said path having a predeterminedcolorant value; means for projecting said particular point on said axis,thus obtaining a projected point; and means for adding said projectedpoint to said look up table as a sampling point.
 12. The systemaccording to claim 11 further comprising said printing device.
 13. Acomputer program for constructing a look up table for characterizing aprinting device, wherein said look up table is an inverse look up tablefor obtaining for said printing device colorant values in a colorantspace as a function of given color values in a color space, the computerprogram comprising code for performing the method of: selecting an axisin said color space; selecting a path in said color space; determining aparticular point on said path having a predetermined colorant value;projecting said particular point on said axis, thus obtaining aprojected point; and adding said projected point to said look up tableas a sampling point.
 14. A computer readable medium comprising programcode adapted to carry out the method of: selecting an axis in said colorspace; selecting a path in said color space; determining a particularpoint on said path having a predetermined colorant value; projectingsaid particular point on said axis, thus obtaining a projected point;and adding said projected point to said look up table as a samplingpoint.
 15. (canceled)